{"id":"https://openalex.org/W2006910694","doi":"https://doi.org/10.1137/s106482750240858x","title":"Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs","display_name":"Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2006910694","doi":"https://doi.org/10.1137/s106482750240858x","mag":"2006910694"},"language":"en","primary_location":{"id":"doi:10.1137/s106482750240858x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750240858x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023907914","display_name":"Hans De Sterck","orcid":"https://orcid.org/0000-0002-1641-932X"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. De Sterck","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008694561","display_name":"Thomas A. Manteuffel","orcid":"https://orcid.org/0000-0002-8897-4146"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas A. Manteuffel","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046048300","display_name":"Stephen F. McCormick","orcid":"https://orcid.org/0000-0002-6327-790X"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen F. McCormick","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027808971","display_name":"Luke N. Olson","orcid":"https://orcid.org/0000-0002-5283-6104"},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luke Olson","raw_affiliation_strings":["Brown University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6721,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.88241191,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"26","issue":"1","first_page":"31","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8768733739852905},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6622821688652039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5489587783813477},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5254756212234497},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4938672184944153},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4872783422470093},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.42829084396362305},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.365070641040802},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.2942360043525696}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8768733739852905},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6622821688652039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5489587783813477},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5254756212234497},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4938672184944153},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4872783422470093},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.42829084396362305},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.365070641040802},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2942360043525696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s106482750240858x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750240858x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.126.971","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~hdesterc/websiteW/Data/publications/journal/SISCLinearLS.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.413.9462","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.9462","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~hdesterc/websiteW/Data/publications/journal/SISCLinearLSold.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.5177","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.5177","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://amath.colorado.edu/pub/fosls/hyp1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7265260469","display_name":"FIRST ORDER SYSTEM LEAST SQUARES (FOSLS):  FUNDAMENTALS AND APPLICATIONS (FAST ALGORITHMS FOR TRANSPORT MODELS)","funder_award_id":"FG02-03ER25574","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8465621227","display_name":"Vertical Integration of Research and Education in Applied   Mathematics","funder_award_id":"9810751","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8952704035","display_name":"TERASCALE OPTIMAL PDE         SIMULATIONS (TOPS) CENTER","funder_award_id":"FC02-01ER25479","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W62043397","https://openalex.org/W70071832","https://openalex.org/W235600206","https://openalex.org/W630841514","https://openalex.org/W1492326914","https://openalex.org/W1493698815","https://openalex.org/W1507767947","https://openalex.org/W1524015806","https://openalex.org/W1530872699","https://openalex.org/W1549057003","https://openalex.org/W1593553932","https://openalex.org/W1603605179","https://openalex.org/W1995000778","https://openalex.org/W1997542937","https://openalex.org/W2003438645","https://openalex.org/W2009985306","https://openalex.org/W2012071009","https://openalex.org/W2012076202","https://openalex.org/W2012492661","https://openalex.org/W2034976587","https://openalex.org/W2039789965","https://openalex.org/W2072819569","https://openalex.org/W2092669265","https://openalex.org/W2093687887","https://openalex.org/W2099656682","https://openalex.org/W2099917284","https://openalex.org/W2132292023","https://openalex.org/W2152033338","https://openalex.org/W2489432230","https://openalex.org/W4205777361","https://openalex.org/W4230108662","https://openalex.org/W4245820193","https://openalex.org/W4300509647"],"related_works":["https://openalex.org/W4386004709","https://openalex.org/W2075755912","https://openalex.org/W2091296067","https://openalex.org/W1527096857","https://openalex.org/W2070999895","https://openalex.org/W2883804816","https://openalex.org/W2049309940","https://openalex.org/W88489855","https://openalex.org/W4298303811","https://openalex.org/W1971658947"],"abstract_inverted_index":{"Least-squares":[0],"finite":[1,101],"element":[2,58],"methods":[3,74,153],"(LSFEMs)":[4],"for":[5,62,76,93,100,113,160],"scalar":[6],"linear":[7,172,197],"partial":[8],"differential":[9],"equations":[10],"(PDEs)":[11],"of":[12,19,43,50,103,143,146,148,163,195],"hyperbolic":[13,178],"type":[14],"are":[15,34,69,96,155,166,182],"studied.":[16],"The":[17,36],"space":[18],"admissible":[20],"boundary":[21],"data":[22],"is":[23,38,55,60,120],"identified":[24],"precisely,":[25],"and":[26,30,47,64,90,109,112],"a":[27,31,44],"trace":[28],"theorem":[29],"Poincar\u00e9":[32],"inequality":[33],"formulated.":[35],"PDE":[37],"restated":[39],"as":[40],"the":[41,48,51,86,114,118,124,144,171,177,193,196],"minimization":[42],"least-squares":[45],"functional,":[46],"well-posedness":[49],"associated":[52],"weak":[53],"formulation":[54],"proved.":[56],"Finite":[57],"convergence":[59,80,137],"proved":[61],"conforming":[63],"nonconforming":[65],"(discontinuous)":[66],"LSFEMs":[67],"that":[68,117,131,154,174,187],"similar":[70],"to":[71,157,170,184,192],"previously":[72],"proposed":[73],"but":[75],"which":[77],"no":[78],"rigorous":[79],"proofs":[81],"have":[82],"been":[83],"given":[84],"in":[85,98,141],"literature.":[87],"Convergence":[88],"properties":[89,138],"solution":[91],"quality":[92],"discontinuous":[94],"solutions":[95],"investigated":[97],"detail":[99],"elements":[102,133],"increasing":[104],"polynomial":[105],"degree":[106],"on":[107],"triangular":[108],"quadrilateral":[110],"meshes":[111],"general":[115],"case":[116],"discontinuity":[119],"not":[121],"aligned":[122],"with":[123],"computational":[125],"mesh.":[126],"Our":[127],"numerical":[128],"studies":[129],"found":[130,183],"higher-order":[132],"yield":[134,185],"slightly":[135],"better":[136],"when":[139],"measured":[140],"terms":[142],"number":[145],"degrees":[147],"freedom.":[149],"Standard":[150],"algebraic":[151],"multigrid":[152],"known":[156],"be":[158],"optimal":[159],"large":[161],"classes":[162],"elliptic":[164],"PDEs":[165],"applied":[167],"without":[168],"modifications":[169],"systems":[173],"result":[175],"from":[176],"LSFEM":[179],"formulations.":[180],"They":[181],"complexity":[186],"grows":[188],"only":[189],"slowly":[190],"relative":[191],"size":[194],"systems.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
